Skip to main content
SpringerLink
Log in

Nested decomposition for dynamic models

  • Published:
Mathematical Programming Submit manuscript

Abstract

This nested decomposition algorithm is intended for solving linear programs with the staircase structure that is characteristic of dynamic multi-sector models for economic development. Staircase problems represent a special case of the discrete-time optimal control problem. Our method is based upon the same principles as that of Glassey [5], but appears easier to describe and to relate to control theory.

Computational experience is reported for a series of test problems. The algorithm has been coded in MPL, an experimental language for mathematical programming. This translator has made it possible to obtain a more readable program — and with fewer instructions — than one written in a conventional language. However, because the present version of MPL does not permit the use of slow access memory, this has prevented us from exploring the full potential of nested decomposition for solving larger problems than can be handled by conventional simplex techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, N.J., 1963).

    Google Scholar 

  2. G.B. Dantzig, T. Magnanti and S. Maier, “A user's guide to MPL/T.1”, Paper No. 76, Graduate School of Business Administration, Duke University, Durham, N.C. (December 1972).

    Google Scholar 

  3. G.B. Dantzig and P. Wolfe, “The decomposition algorithm for linear programs”,Econometrica 29 (1961) 767–778.

    Google Scholar 

  4. C.R. Glassey, “Nested decomposition and multi-stage linear programs”,Management Science 20 (1973) 282–292.

    Google Scholar 

  5. C.R. Glassey, “Dynamic linear programs for production scheduling”,Journal of the Operations Research Society of America 19 (1971) 45–56.

    Google Scholar 

  6. H. Halkin, “A maximum principle of the Pontryagin type for systems described by nonlinear difference equations”,SIAM Journal on Control 4 (1966) 90–111.

    Google Scholar 

  7. A.S. Manne, “Sufficient conditions for optimality in an infinite horizon development plan”,Econometrica 38 (1970) 18–38.

    Google Scholar 

  8. M. Simmonard,Linear programming (Prentice-Hall, Englewood Cliffs, N.J., 1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Stanford University, Stanford, Calif., USA

    James K. Ho & Alan S. Manne

Authors
  1. James K. Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan S. Manne
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Prepared under National Science Foundation Grant GS-30377 at the Institute for Mathematical Studies in the Social Sciences, Stanford University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ho, J.K., Manne, A.S. Nested decomposition for dynamic models. Mathematical Programming 6, 121–140 (1974). https://doi.org/10.1007/BF01580231

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01580231

Keywords

Search

Navigation